Answered: - Use Euler's inequality (m≤3n-6) to…

- Use Euler's inequality (m≤3n-6) to prove that each planar graph has at least two vertices of degree at most 5. (Can you do better than 2?)

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Convex Hull

For a given set of points S in a plane, the convex hull is a line completely enclosing all the points within the plane such that no concavities are left. In other words, the convex hull of a set of points is the smallest convex polygon consisting of all points within the plane.

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Use Euler's inequality (m≤ 3n-6) to prove that each planar graph has at least two
vertices of degree at most 5. (Can you do better than 2?)

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